1. Field of Invention
This invention relates to processing acoustic reflections to obtain velocity information for an acoustic medium and, in particular, processing seismic data to obtain a velocity field.
2. Description of Related Art
Acoustic energy in the form of reflected acoustic waves, such as conventional seismic reflections, are often detected and then processed to obtain a three-dimensional (3D) seismic velocity field associated with a 3D region within the earth's subsurface. The 3D velocity field typically includes velocity values approximating the velocity of a seismic wave travelling through corresponding points within the 3D region. The 3D velocity field may alternatively be expressed as a set of time-velocity curves. Each time-velocity curve is typically associated with a location on a surface of the 3D region and includes velocity values and associated time values. The time values represent the two-way travel time of sound along a path from a source, to a subsurface point and back to a receiver. The corresponding velocity value represents the velocity of sound travelling through the subsurface point.
Particular paths which have importance in seismic imaging include the “Normal Ray” path, which is the path followed by a Snell ray starting normal to a subsurface planar reflecting surface and travelling to the surface. Another important particular path is the “Image Ray” path, which is the path followed by a Snell ray starting normal to the surface and travelling downward to a subsurface point. Both rays obey Snell's Law as dictated by the acoustic wave equation (see O. Yilmaz, Seismic Data Processing, in S. M. Doherty, ed., Investigations in Geophysics No. 2 (Society of Exploration Geophysicists); S. M. Deregowski, “Common-Offset Migrations and Velocity Analysis”, First Break, vol. 8, No. 6, June 1990, pp. 225-234; and P. Hubral, “Time Migration”—Some Theoretical Aspects”, 1977, Geophysical Prospecting, pp. 738-745).
Producing seismic data conventionally includes detecting back scattered energy including seismic reflections and diffractions acquired from source-receiver pairs acting on a surface of the 3D region. Incident seismic waves are sequentially generated in the earth's subsurface by one or more sources of seismic energy and are each partially reflected or diffracted back from seismic scatterers, including for example strata interfaces, located at a distance from the surface equal to the depth of the seismic scatterer. Each seismic scatterer can be considered a reflection surface that may be parallel to the surface and referred to as a horizontal seismic reflector, or may be at an angle relative to the surface, known as a dipping angle. Each incident seismic wave, once reflected, is referred to as a seismic reflection. The seismic reflections generated from each sequentially acting seismic source reach different locations on the surface of the earth at different times, depending on the distance and velocity characteristics of the subsurface traversed. Each of one or more seismic receivers is used to produce a respective electrical signal representing the seismic reflections received at a location on the surface. Each electrical signal is often represented digitally as a time-amplitude representation that includes amplitude values associated with respective time values. The time-amplitude representation is referred to as a seismic trace. Each seismic trace is typically associated with the respective locations of the seismic source and receiver.
The seismic data may be divided into subsets conventionally referred to as common mid-point (CMP) gathers. Each CMP gather includes seismic traces associated with the same CMP location. The CMP location of a CMP gather is defined as the location mid-way between respective source and receiver locations of the source-receiver pairs that acted in producing the seismic traces making up the CMP gather. The seismic traces of each CMP gather are also associated with respective offset values. The offset value is the distance between the respective source and receiver locations of the source-receiver pair.
A normal moveout (NMO) operation may be performed on the seismic traces within a given CMP gather to time shift each amplitude value of each seismic trace of the given CMP gather according to the relation:t2(x)=t2(0)+x2/ν2 where    t(x) is the time value associated with the amplitude value before the NMO operation;    t(0) is a zero-offset time value associated with the amplitude value after the NMO operation;    X is an offset value associated with the seismic trace; and    ν is a velocity value associated with a time value equal to t(0).
If an accurate time-velocity curve is used for an NMO operation applied to a CMP gather, then the resulting amplitude values produced from seismic reflections of the same seismic reflector will be associated with the same zero-offset time value and will be aligned at that zero-offset time after NMO. If, on the other hand, an inaccurate time-velocity curve is used for the NMO operation, the resulting amplitude values produced from seismic reflections of the same seismic reflector will not be aligned in time and the resulting CMP gather is said to have residual moveout. The extent to which the resulting amplitude values do not align in time indicates the extent of residual moveout.
Conventional velocity analysis includes manual and automatic velocity analysis. Conventional manual velocity analysis on each CMP gather may involve applying several NMO operations to the CMP gather, each NMO operation being performed using one time-velocity curve of a predetermined set of different time-velocity curves. The resulting CMP gathers are presented graphically to a velocity analysis expert who selects the resulting CMP gather for which the least amount of residual moveout is apparent from the graphical presentation. Manual velocity analysis requires the services of a velocity analysis expert, is time consuming, and often results in less than accurate estimates of velocity, especially when a limited number of different time-velocity curves is used.
Conventional automatic velocity analysis on each CMP gather may involve using an initial time-velocity curve to apply an NMO operation to the CMP gather to produce a resulting CMP gather, applying a stacking operation to the resulting CMP gather by summing the amplitude values of the respective time-amplitude traces of the resulting CMP gather to produce a stacked amplitude trace, modifying velocity values of the initial time-velocity curve, and iteratively producing stacked amplitude traces until a stacked amplitude trace having maximum stacked amplitudes is obtained. The time-velocity curve used to produce the stacked amplitude stack with maximum amplitudes is taken to be the most accurate time-velocity curve associated with the CMP. The process must be repeated for each CMP location on the surface to produce an optimal 3D velocity field. Such automatic velocity analysis requires an exorbitantly large number of iterations and is therefore computationally expensive.
Rather than optimizing an initial time-velocity curve for each CMP location, automatic velocity analysis may iteratively optimize an initial 3D velocity field. Such automatic velocity analysis may involve simultaneously maximizing stacked amplitude values of stacked amplitude traces associated with all CMP locations of interest. Such automatic velocity analysis, however, either risks instability, potentially converging to a local extremum or not converging at all, or requires a large number of iterations to stably converge to an optimal 3D velocity field.